Mathematical Logic digital book with solutions

Q. 1/88· Easy

If a compound statement is false for all its component, then the compound statement is a

Q. 2/88· Easy

Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

Q. 3/88· Easy

$p\rightarrow q$ is logically equivalent to

Q. 4/88· Easy

Consider the following statements

(i) If $x>20$ , then $x>10$

(ii) If $x\not>20$ , then $x\not>10$

(iii) If $x>10$ , then $x>20$

(iv) If $x\not>10$ , then $x\not>20$

The pair of statement having the same meaning is

Q. 5/88· Easy

Negation of the statement $\exists n\in R$ , such that $n+5>8$ is

Q. 6/88· Easy

The converse of the proposition 'If an integer is greater than 30 , then it is greater than 10' is

Q. 7/88· Easy

If $A=\{1,2,3,4,5,6\}$ then which of the following is not true?

Q. 8/88· Easy

Contrapositive of the statement. 'If two numbers are equal, then their squares are equal' is

Q. 9/88· Easy

The converse of "If 3 is a prime number, then 3 is odd." is

Q. 10/88· Easy

The compound proposition $(p\land q)\rightarrow p$ is

Q. 11/88· Easy

$p\leftrightarrow q$ is logically equivalent to

Q. 12/88· Easy

If $x-3=11$ is open sentence defined on set of natural numbers $N$ , then the corresponding true statement is

Q. 13/88· Easy

Which of the following are equivalent statements?

(i) $p\rightarrow q$

(ii) $\sim p\lor q$

(iii) $\sim q\rightarrow\sim p$

(iv) $(p\rightarrow q)\land(q\rightarrow p)$

Q. 14/88· Easy

If $A=\{1,2,3,4,5\}$ , then which of the following statements is not true?

Q. 15/88· Easy

The statement pattern $(p \wedge q) \rightarrow(r \vee \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively